Cremona's table of elliptic curves

840 = 2³ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 7+	Signs for the Atkin-Lehner involutions
Class	840c	Isogeny class
Conductor	840	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	107520 = 210 · 3 · 5 · 7	Discriminant
Eigenvalues	2+ 3+ 5- 7+  0  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2240,-40068]	[a1,a2,a3,a4,a6]
j	1214399773444/105	j-invariant
L	1.3878783222606	L(r)(E,1)/r!
Ω	0.69393916113032	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1680i3 6720p3 2520o3 4200z3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 840c3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	+	-	+	0	2	2	0	0	6	4	-2	10	4	0	2	4	6	-12	12	-2	0	4	10	-2

---

Quadratic twists for elliptic curve 840c3

-4	8	-3	5	-7	-11
1680i3	6720p3	2520o3	4200z3	5880k3	101640ce4

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations